13. (18 pts) The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for x 2 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.02x for 0 5 x 5 2250. In Quiz 2, problem #10, we saw that the profit function for this scenario is P(x) = - 0.02x2+ 38.00x- 5250. (a) The profit function is a quadratic function and so its graph is a parabola. Does the parabola open up or down? (b) Find the vertex of the profit function P(x) using algebra. Show algebraic work. (c) State the maximum profit and the number of widgets which yield that maximum profit: The maximum profit is when widgets are produced and sold. (d) Determine the price to charge per widget in order to maximize profit. (e) Find and interpret the break-even points. Show algebraic work